Dynamical phase of driven colloidal systems with short-range attraction and long-range repulsion

We study the nonequilibrium dynamics of colloidal system with short-range depletion attraction and screened electrostatic repulsion on a disordered substrate. We find a growth-melting process of the clusters as the temperature is increased. By strengthening the screened electrostatic repulsion, a depinning transition from moving cluster to plastic flow is observed, which is characterized by a peak in threshold depinning force. The corresponding phase diagram is then mapped out. Due to the influences of disorder from substrate, the clusters are polarized by the strong external force, accompanied by the appearance of interesting orientational order parallel to the force and translational order perpendicular to the force. Under the condition of strong external force, the influences of density of pins and temperature are also studied.     

Inherent structures for soft long-range interactions in two-dimensional many-particle systems

We generate inherent structures, local potential-energy minima, of the "k-space overlap potential" in two-dimensional many-particle systems using a cooling and quenching simulation technique. The ground states associated with the k-space overlap potential are stealthy (i.e., completely suppress single scattering of radiation for a range of wavelengths) and hyperuniform (i.e., infinite wavelength density fluctuations vanish). However, we show via quantitative metrics that the inherent structures exhibit a range of stealthiness and hyperuniformity depending on the fraction of degrees of freedom χ that are constrained. Inherent structures in two dimensions typically contain five-particle rings, wavy grain boundaries, and vacancy-interstitial defects. The structural and thermodynamic properties of the inherent structures are relatively insensitive to the temperature from which they are sampled, signifying that the energy landscape is relatively flat along the directions sampled, with wide shallow local minima and devoid of deep wells. Using the nudged-elastic-band algorithm, we construct paths from ground-state configurations to inherent structures and identify the transition points between them. In addition, we use point patterns generated from a random sequential addition (RSA) of hard disks, which are nearly stealthy, and examine the particle rearrangements necessary to make the configurations absolutely stealthy. We introduce a configurational proximity metric to show that only small local, but collective, particle rearrangements are needed to drive initial RSA configurations to stealthy disordered ground states. These results lead to a more complete understanding of the unusual behaviors exhibited by the family of "collective-coordinate" potentials to which the k-space overlap potential belongs.     

A molecular-dynamics simulation study on the dependence of Lennard-Jones gas-liquid phase diagram on the long-range part of the interactions

The particle-transfer molecular-dynamics technique is adopted to construct the Lennard-Jones fluid gas-liquid phase diagram. Detailed study of the dependence of the simulation results on the system size and the cutoff distance is performed to test the validity of the simulation technique. Both the traditional cutoff plus long-range correction (CPC) and Ewald summation methods are used in the simulations to calculate the interactions. In the intermediate range of temperatures, the results with the Ewald summation method are almost the same as those with the CPC method. However, in the range close to the critical point, the results with the CPC method deviate from those with the Ewald summation. Compared with the results obtained via the Ewald summation in a smaller system, simply increasing the system size in the CPC scheme may not give better results.     

Experimental phase diagram of symmetric binary colloidal mixtures with opposite charges

The phase behavior of equimolar mixtures of oppositely charged colloidal systems with similar absolute charges is studied experimentally as a function of the salt concentration in the system and the colloid volume fraction. As the salt concentration increases, fluids of irreversible clusters, gels, liquid-gas coexistence, and finally, homogeneous fluids, are observed. Previous simulations of similar mixtures of Derjaguin-Landau-Verwey-Overbeek (DLVO) particles indeed showed the transition from homogeneous fluids to liquid-gas separation, but also predicted a reentrant fluid phase at low salt concentrations, which is not found in the experiments. Possibly, the fluid of clusters could be caused by a nonergodicity transition responsible for the gel phase in the reentrant fluid phase. Liquid-gas separation takes a delay time after the sample is prepared, whereas gels collapse from the beginning. The density of the liquid in coexistence with a vapor phase depends linearly on the overall colloid density of the system. The vapor, on the other hand, is comprised of equilibrium clusters, as expected from the simulations.     

The phase diagram of charged colloidal lipid A-diphosphate dispersions

Small-angle X-ray-scattering, light-scattering, and electron microscope experiments were used to determine the phase transitions of colloidal lipid A-diphosphate aqueous dispersions. The phases detected were a correlated liquid phase, a face-centered cubic (Fd3m) and a body-centered cubic (Im3m) colloidal crystal phase and a new glass phase. These experimentally determined phases were shown to be in accord with theoretically predicted equilibrium phases.     

Microphase separation in two-dimensional systems with competing interactions

The formation of clusters in condition of thermodynamic equilibrium can be easily observed both in two and three dimensions. In two dimensions relevant cases include pattern formation in Langmuir monolayers and ferrofluids, while in three dimensions cluster phases have been observed in colloids and in protein solutions. We have analyzed the problem within the scenario of competing interactions: typically, a short-range attractive interaction against a long-range repulsive one. This simplified approach is suggested by the fact that the forces, governing self-organization, act on a length scale which is larger than the molecular size; as a consequence many specific details of the molecules of interest are not necessary for studying the general features of microphases. We have tackled the microphase formation by simulations in bidimensional fluids, exploiting the parallel tempering scheme. In particular, we have analyzed the density range in which the particles arrange in circular domains (droplets), and the temperature range in which the system goes from microphases to the homogeneous fluid phase. As the density increases, the droplet size increases as well, but above a certain density the morphology changes and stripes are formed. Moreover at low density, we observe the formation of a liquidlike phase of disordered droplets; at higher densities, instead, the droplets tend to arrange onto a triangular superlattice. Such a change affects the features of the static structure factor, which gives well defined signatures of the microphase morphology. In each case, the specific heat exhibits a peak close to the transition from microphases to the homogeneous fluid phase, which is due to the breaking up of the clusters. The saturation of the height of the specific heat peak, with the increasing of the system size, suggests the possibility of a Kosterlitz-Thouless transition.     

Liquid-vapor phase diagram and cluster formation of two-dimensional ionic fluids

Direct molecular dynamics simulations on interfaces at constant temperature are performed to obtain the liquid-vapor phase diagram of the two-dimensional soft primitive model, an equimolar mixture of equal size spheres carrying opposite charges. Constant temperature and pressure simulations are also carried out to check consistency with interface simulations results. In addition, an analysis of the cluster formation of mixtures of particles with charge asymmetry in the range 1:1 to 1:36 at low and high densities is performed. The number of free ions, when plotted as a function of the positive ion charge, Z(+), has an oscillatory behavior and is independent of the density. The formation of aggregates is analyzed in terms of the attraction and repulsion between ions.     

Force constants and many-body electrostatic interactions in two-dimensional colloidal crystal

A model of a two-dimensional colloidal crystal with a hexagonal lattice, the electrostatic interactions in which are described by the nonlinear Poisson-Boltzmann equation, is considered. The calculation procedure for force constants of this crystal is treated in detail. Properties of system symmetry, which make it possible to significantly decrease the volume of calculations and to classify force constants, are analyzed. Numerical data for force constants of a crystal as functions of lattice parameters at different particle sizes are reported. A method that allows us to disclose the presence of many-body interactions in a system by the behavior of force constants at some interval of the values of lattice parameters is proposed. The application of this method to the system under consideration demonstrated that electrostatic interparticle interactions in the system cannot be reduced to simply a pair interaction of any kind; the introduction of many-body potentials is required for the adequate representation of the elastic properties of a crystal.     

Effects of three-body intermolecular interactions on the nematic—paranematic phase diagram

An extension of the Maier—Saupe theory of the nematic—isotropic transition in liquid crystals, which incorporates three-body intermolecular interactions into the effective single-particle pseudopotential, is presented. Numerical calculations based on this theory are performed to investigate the effect of these three-body interactions on the nematic—isotropic transition in zero field, on the nematic—paranematic coexistence curve in the presence of an applied field, and on the mean field nematic—paranematic critical point. The zero field results are in good agreement with experimental measurements.     

Measuring colloidal interactions with confocal microscopy

We use confocal laser scanning microscopy to measure interactions in colloidal suspensions. By inverting the radial distribution function, determined by tracking the particle coordinates, we obtain the effective interaction between the colloidal particles. Although this method can be applied to arbitrary colloidal interactions, here we demonstrate its efficacy with two well-known systems for which accurate theories are available: a colloid-polymer mixture and binary hard spheres. The high sensitivity of this method allows for the precise determination of complex interactions, as exemplified, for example, by the accurate resolution of the oscillatory effective potential of the binary hard sphere system. We argue that the method is particularly well suited for the determination of attractive forces.     

Observation of long-range f-f interactions between two f-electronic systems in quadruple-decker phthalocyanines

Homo and heteronuclear quadruple-decker phthalocyanine tetramers containing Y(3+) and/or magnetically anisotropic lanthanide ions such as Tb(3+), Dy(3+), and Er(3+) have been synthesized, and their magnetic properties have been elucidated, giving clear evidence of the long-range interactions between two f-electronic centers.     

Role of polydispersity in anomalous interactions in electrostatically levitated colloidal systems

In this paper, we investigate the effects of using inverse analyses developed for monodisperse particles to extract particle-particle and particle-surface potentials from simulated interfacial colloidal configurations having finite-size polydispersity. Forward Monte Carlo simulations are used to generate three-dimensional equilibrium configurations of log normal-distributed polydisperse particles confined by gravity near an underlying surface. Particles remain levitated above the substrate and stabilized against aggregation by repulsive electrostatic Derjaguin-Landau-Verwey-Overbeek pair potentials. An inverse Ornstein-Zernike analysis and an inverse Monte Carlo simulation method are used to obtain interactions from simulated distribution functions as a function of polydispersity (sigma), relative range of repulsion (kappa a), and projected interfacial concentration (rho). Both inverse analyses successfully recover input potentials for all monodisperse cases, but fail for polydispersities often encountered in experiments. For different conditions (sigma, kappa a, and rho), our results indicate softened short-range repulsion, anomalous long-range attraction, and apparent particle overlaps, which are similar to commonly reported observations in optical microscopy measurements of quasi-two-dimensional interfacial colloidal ensembles. By demonstrating signatures of, and limitations due to, polydispersity when extracting pair potentials from measured distribution functions, our specific goal is to provide a basis to objectively interpret and resolve the effects of polydispersity in optical microscopy experiments.     

Transition metal-chalcogen systems,VI: The zirconium-tellurium phase diagram

In the binary Zr–Te system isopiestic, thermoanalytical, and X-ray studies were carried out. The results were combined with data from literature to construct a partial phase diagram. Tetragonal Zr₅Te₄ exists at 44.4 at %Te. Hexagonal ZrTe (WC structure) with a composition between 49 and 50 at %Te is found from 723 to 1,273 K. NiAs-type Zr _1–x Te has a range of homogeneity above 1,273 K from 52.0 to 66.6 at %Te, and at 973 and 723 K from 57.0 to 66.6 at %Te. Within this range the NiAs-type structure transforms into the Cd(OH)₂-type structure. At 60 at %Te Zr _1–x Te has a melting point of about 1,970 K. At 75 at %Te monoclinic ZrTe₃ is found which decomposes peritectically at 903 K. At 778 K orthorhombic ZrTe₅ transforms into liquid and ZrTe₃, and at 712 K ZrTe₅ forms a eutectic with Te.

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Übergangsmetall-Chalcogen-Systeme, 6. Mitt.: Das Zirkonium-Tellur-Phasendiagramm

Zusammenfassung Im binären Zr–Te-System wurden isopiestische, thermoanalytische und röntgenographische Untersuchungen durchgeführt. Die Resultate wurden mit Literaturdaten kombiniert und ein partielles Phasendiagramm aufgestellt. Tetragonales Zr₅Te₄ existiert bei 44.4 At %Te. Hexagonales ZrTe (WC-Struktur) mit einer Zusammensetzung zwischen 49 und 50 At %Te ist zwischen 723 und 1273 K beständig. Zr _1–x Te mit NiAs-Struktur hat oberhalb 1273 K einen Homogenitätsbereich von 52.0 bis 66.6 At %Te, bei 973 und 723 K einen solchen von 57.0 bis 66.6 At %Te. Innerhalb dieses Bereiches geht die NiAs-Struktur in die Cd(OH)₂-Struktur über. Zr _1–x Te mit einer Zusammensetzung von 60 At %Te hat einen Schmelzpunkt von etwa 1,970 K. Bei 75 At %K. wurde monoklines ZrTe₃ gefunden, welches bei 903 K peritektisch zerfällt. Bei 778 K reagiert orthorhombisches ZrTe₅ zu ZrTe₃ und Schmelze, bei 712 K bildet ZrTe₅ mit Te ein Eutektikum.

     

Transition metal-chalcogen systems,VII.: The iron-selenium phase diagram

The binary iron-selenium system was investigated by thermoanalytical and isopiestic methods and by X-ray analysis. Combining all results a temperature-concentration diagram was constructed from 20 to 66 at% Se and between 623 and 1,373 K. Two compounds and several NiAs-related structures could be identified. Tetragonal -FeSe with a narrow stability range between 49.0 and 49.4 at% Se at 653 K decomposes by a peritectoid reaction at 730 K. The NiAs-related structures Fe_1-x Se have a wide range of homogeneity from 51.5 to 58.5 at% Se at 823 K. The iron-rich hexagonal -phase extends, from 51.5 to 54.3 at% Se, and transforms to a high temperature modification of unknown structure with a maximum transformation temperature of 1,338 K at 52.8 at% Se. The congruent melting point of the -phase is located at 1,351 K and 52.0 at% Se. At 54 at% Se the -phase undergoes a -transformation to the monoclinic -phase which is stable between 54.3 and 54.6 at% Se. Between 54.6 and 56.4 at% Se two very similar monoclinic phases coexist: the -and the -phase with similara- andb-axes but a simplec- and a doublec-axis, resp. Between 56.4 and 58.5 at% Se the -phase is stable. Orthorhombic -FeSe₂ (marcasite structure) with a very narrow range of homogeneity at 66.6, at% Se decomposes peritectically at 858 K. On the iron-rich side there are three invariant equilibria at high temperatures: a monotectic at 1,234 K and 46.5 at% Se, a eutectic at 1,215 K and 5.5 at% Se, and a eutectoid at 1,149 K. On the selenium-rich side there is a eutectoid at 1,122 K, a monotectic at 1,068 K and 71.5 at% Se, and a peritectic at 1,001 K.

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Übergangsmetall-Chalcogen-Systeme, 7. Mitt.: Das Eisen-Selen-Phasen-Diagramm

Zusammenfassung Das Zweistoffsystem Eisen-Selen wurde thermisch, röntgenographisch und isopiestisch untersucht. Aus den Ergebnissen konnte dasT-x-Zustands-diagramm für den Bereich von 20 bis 66 At%Se und von 623 bis 1 373 K erstellt werden. Zwei Verbindungen und einige, NiAs-ähnliche Strukturen konnten identifiziert werden. Die tetragonale -Phase FeSe besitzt bei 653 K eine schmale Phasenbreite von 49,0 bis 49,4 At%Se und zerfällt peritektoidisch bei 730 K. Die NiAs-ähnlichen Strukturen Fe_1-x Se haben bei 823 K einen breiten Homogenitätsbereich von 51,5 bis 58,5 At%Se. Die eisenreiche hexagonale -Phase reicht von 51,5 bis 54,3 At%Se und wandelt sich bei 1 338 K und 52,8 At%Se in eine Hochtemperaturmodifikation mit unbekannter Struktur, die -Phase, um, deren kongruenter Schmelzpunkt bei 52,0 At%Se und 1 351 K liegt. Bei etwa 54 At%Se geht das hexagonale Gitter infolge einer -Umwandlung in die monokline -Phase über, welche von 54,3 bis 54,6 At%Se reicht. Zwischen 54,6 und 56,4 At%Se liegt ein Zweiphasengebiet von zwei sehr ähnlichen monoklinen Phasen: die -und die -Phase mit ähnlichena- undb-Parametern, aber einfacherc-bzw. doppelterc-Achse. Die monokline -Phase befindet sich zwischen 56,4 und 58,5 At%Se. Die orthorhombische -Phase FeSe₂ mit Markasitstruktur mit einem sehr engen Homogenitätsbereich bei 66,6 At%Se zerfällt peritektisch bei 858 K. An der eisenreichen Seite gibt es bei höheren Temperaturen drei invariante Gleichgewichte: ein Eutektikum bei 5,5 At%Se und 1 215 K, ein Monotektikum bei 46,5 At%Se und 1 234 K und ein Eutektoid bei 1 149 K. An der selenreichen Seite existiert bei 71,5 At%Se und 1 068 K ein Monotektikum, bei 1 122 K ein Eutektoid und bei 1 001 K ein Peritektikum.

     

Assembling and manipulating two-dimensional colloidal crystals with movable nanomagnets

We study crystallization of paramagnetic beads in a magnetic field gradient generated by one-dimensional nanomagnets. The pressure in such a system depends on both the magnetic forces and the hydrodynamic flow, and we estimate the flow threshold for disassembling the crystal near the magnetic potential barrier. A number of different defects have been observed which fluctuate in shape or propagate along the crystal, and it is found that the defect density increases away from the nanomagnet. We also study the melting of the crystal/fluid system after removal of the nanomagnet and demonstrate that the bond-oriental order parameter decreases with time. The nanomagnet can be moved in a controlled manner by a weak external magnetic field, and at sufficiently large driving velocities we observe self-healing crack formation characterized by a roughening of the lattice as well as gap formation. Finally, when confined between two oscillating nanomagnets, the colloidal crystal is shown to break up and form dipolar chains above a certain oscillation frequency.     

Phase diagram of a two-dimensional system with anomalous liquid properties

Using Monte Carlo simulation techniques, we calculate the phase diagram for a square-shoulder square-well potential in two dimensions that has been previously shown to exhibit liquid anomalies consistent with a metastable liquid-liquid critical point. We consider the liquid, gas, and five crystal phases, and find that all the melting lines are first order, despite a small range of metastability. One melting line exhibits a temperature maximum, as well as a pressure maximum that implies inverse melting over a small range in pressure.     

Effect of long-range interactions on the surface tension

The effect of long-range interactions on the surface tension at a liquid-gas interface was considered. An analytical expression for the correction to the surface tension for the cutoff of the particle interaction potential at the distance r _c was derived based on a step density profile. For the Lennard-Jones fluid, this correction was calculated numerically from the results of computer simulations of the density profiles. It was established that, in the vicinity of the triple point, the correction is as great as ～6% at the potential cutoff radius r _c=6.78 molecular diameters, a quantity insensitive to the form of the density profile in the interfacial layer.     

Neutral-ionic interface in charge-transfer salts with long-range coulomb interactions

Coulomb interactions - Vα stabilize both neutral and ionic lattices against charge-transfer (CT) excitations for Madelung-constant α>1. The neutral-ionic phase boundary δ_c(χ) and ionicity jump Δq(χ) are accurately given by the lowest-order corrections in χ = ¦t¦/V(α-1) for χ ⩽ 0.2 and Mulliken CT integral t. Numerical solutions of (2N ⩽ 18)-site DA rings, with D²⁺ and A²⁻ excluded, show Δq(χ) to vanish for χ > χ_c = 0.33±0.02, where δ_c/¦t¦=0.39±0.02, in contrast to δ_c = 0 in two-state models that neglect the D⁺ and A⁻ spins.